Question

convert decimal to binary numbers : (a) (84)10. (b) (106)10. (c) (256)10.

Answer 1

$\textbf{Answer :}$

(a) 84 (10) = ? (2)
_____________

84/2 = 42 (remainder = 0)
42/2 = 21 (remainder = 0)
21/2 = 10 (remainder = 1)
10/2 = 5 (remainder = 0)
5/2 = 2 (remainder = 1)
2/2 = 1 (remainder = 0)
1/2 = 0 (remainder = 1)

Therefore,
84 (10) = 1010100 (2)

(b) 106 (10) = ? (2)
_____________

106/2 = 53 (remainder = 0)
53/2 = 26 (remainder = 1)
26/2 = 13 (remainder = 0)
13/2 = 6 (remainder = 1)
6/2 = 3 (remainder = 0)
3/2 = 1 (remainder = 1)
1/2 = 0 (remainder = 1)

Therefore,
106 (10) = 1101010 (2)

(c) 256 (10) = ? (2)
_____________

256/2 = 128 (remainder = 0)
128/2 = 64 (remainder = 0)
64/2 = 32 (remainder = 0)
32/2 = 16 (remainder = 0)
16/2 = 8 (remainder = 0)
8/2 = 4 (remainder = 0)
2/2 = 1 (remainder = 0)
1/2 = 0 (remainder = 1)

Therefore,
256 (10) = 10000000 (2)

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Answer 2

Answer:

(a) 84 (10) = ? (2)

_____________

84/2 = 42 (remainder = 0)

42/2 = 21 (remainder = 0)

21/2 = 10 (remainder = 1)

10/2 = 5 (remainder = 0)

5/2 = 2 (remainder = 1)

2/2 = 1 (remainder = 0)

1/2 = 0 (remainder = 1)

Therefore,

84 (10) = 1010100 (2)

(b) 106 (10) = ? (2)

_____________

106/2 = 53 (remainder = 0)

53/2 = 26 (remainder = 1)

26/2 = 13 (remainder = 0)

13/2 = 6 (remainder = 1)

6/2 = 3 (remainder = 0)

3/2 = 1 (remainder = 1)

1/2 = 0 (remainder = 1)

Therefore,

106 (10) = 1101010 (2)

(c) 256 (10) = ? (2)

_____________

256/2 = 128 (remainder = 0)

128/2 = 64 (remainder = 0)

64/2 = 32 (remainder = 0)

32/2 = 16 (remainder = 0)

16/2 = 8 (remainder = 0)

8/2 = 4 (remainder = 0)

2/2 = 1 (remainder = 0)

1/2 = 0 (remainder = 1)

Therefore,

256 (10) = 10000000 (2)

Explanation:

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